Admiralty Office

An Admiralty Office can be found in each of the NationalCapital Cities, which can be accessed by any player.
The primary contacts there will include a Prize Agent whom will exchange your Marks of Victory and/or Marks of Trade as well as one or more Naval Commanders, one of which whom will offer rewards for the Citations of Conquest obtained after a Map Victory by any particular Nation. He also offers various Ship upgrades, if you have collected any Magistrate's Marks of Excellence.

The Overhead port map has hover over icons visible which you can click upon to have a directional guide assist you through the streets.

As complex as the French's Capital Pointe-à-Pitre street layout is, the Admiralty is found past the Shop from the Docks off to the far left, then head up the spiral staircase through the first archway. Ascend a few more stairs and you should be able find the recognizably marked door.

The Pirate Nation's equivalent would be Captain Kidd's Quarters.

As far as any of the other non default Pirate city, each has a lesser version often worth stopping by to see if the port's Naval presence has missions for you to complete.